The completeness of eigenfunctions and associated functions of an ordinary differential operator with irregular-separated boundary conditions

1977 ◽  
Vol 10 (4) ◽  
pp. 305-316 ◽  
Author(s):  
A. A. Shkalikov
Keyword(s):  
Differential Operator ◽  
Boundary Conditions ◽  
Ordinary Differential Operator ◽  
Associated Functions ◽  
Separated Boundary Conditions ◽  
Eigenfunctions And Associated Functions ◽  
Completeness Of Eigenfunctions

scholarly journals Basis Properties of Eigenfunctions of Second-Order Differential Operators with Involution

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Asylzat Kopzhassarova ◽  
Abdizhakhan Sarsenbi
Keyword(s):  
Differential Operator ◽  
Differential Operators ◽  
Second Order ◽  
Ordinary Differential Operator ◽  
Spectral Problems ◽  
Associated Functions ◽  
Eigenfunctions And Associated Functions

We study the basis properties of systems of eigenfunctions and associated functions for one kind of generalized spectral problems for a second-order ordinary differential operator.

scholarly journals On Stability of Basis Property of Root Vectors System of the Sturm-Liouville Operator with an Integral Perturbation of Conditions in Nonstrongly Regular Samarskii-Ionkin Type Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
N. S. Imanbaev
Keyword(s):  
Boundary Conditions ◽  
Liouville Operator ◽  
Basis Property ◽  
Differentiation Operator ◽  
Stability And Instability ◽  
Associated Functions ◽  
Sturm Liouville ◽  
Type Boundary ◽  
Eigenfunctions And Associated Functions ◽  
Integral Perturbation

We study a question on stability and instability of basis property of system of eigenfunctions and associated functions of the double differentiation operator with an integral perturbation of Samarskii-Ionkin type boundary conditions.

Asymptotic formulas with arbitrary order for nonselfadjoint differential operators

2007 ◽  
Vol 44 (3) ◽  
pp. 391-409 ◽  
Author(s):  
Melda Duman ◽  
Alp Kiraç ◽  
Oktay Veliev
Keyword(s):  
Differential Operator ◽  
Boundary Conditions ◽  
Differential Operators ◽  
Arbitrary Order ◽  
Ordinary Differential Operator ◽  
Asymptotic Formulas ◽  
Eigenvalues And Eigenfunctions ◽  
Order Of Accuracy ◽  
Strongly Regular

We obtain asymptotic formulas with arbitrary order of accuracy for the eigenvalues and eigenfunctions of a nonselfadjoint ordinary differential operator of order n whose coefficients are Lebesgue integrable on [0, 1] and the boundary conditions are strongly regular. The orders of asymptotic formulas are independent of smoothness of the coefficients.

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